Elitzur–Vaidman bomb tester

The Elitzur–Vaidman bomb-tester is a quantum mechanics thought experiment that uses interaction-free measurements to verify that a bomb is functional without having to detonate it.

Since their publication, real-world experiments have confirmed that their theoretical method works as predicted.

[1] The bomb tester takes advantage of two characteristics of elementary particles, such as photons or electrons: nonlocality and wave–particle duality.

[2] By placing the particle in a quantum superposition, it is possible for the experiment to verify that the bomb works without triggering its detonation, although there is still a 50% chance that the bomb will detonate in the effort.

This gleaning of information is possible even if the particle was never factually in any of the particular states or locations that are of interest.

Is it possible to determine which bombs are functional and which are duds without detonating all of the live ones?

Along both the upper and lower path, the particle will encounter an ordinary mirror, positioned to redirect the two routes toward one another.

If it is a dud, the photon will pass by unaffected (see figure 4), i.e., it will remain in superposition until it reaches a detector.

To understand how this experiment works, it is important to know that unlike a dud, a live bomb is a kind of observer and that an encounter between the photon and a live bomb is a kind of observation.

But, like the radioactive material in the box with Schrödinger's famous cat, upon its encounter with the half-silvered mirror at the beginning of the experiment, the photon, paradoxically does and does not interact with the bomb.

When it reaches the second half-silvered mirror, if the photon in the experiment is behaving like a particle (in other words, if it is not in a superposition), then it has a fifty-fifty chance it will pass through or be reflected and be detected by one or the other detector.

In other words, if the photon is in a superposition at the time it arrives at the second half-silvered mirror, it will always arrive at detector C and never at detector D. If the bomb is live, there is a 50/50 chance that the photon took the upper path.

At which point it will, again, have a 50/50 chance of passing through it or being reflected off it, and, subsequently, it will be detected at either of the two detectors with the same probability.

This is what makes it possible for the experiment to verify the bomb is live without actually blowing it up.

The probability of exploding the bomb can be made arbitrarily small by repeating the interaction several times.

[9][10] Assume that a box which potentially contains a bomb is defined to operate on a single probe qubit in the following way: The following quantum circuit can be used to test if a bomb is present: Where: At the end of the circuit, the probe qubit is measured.

The probability of obtaining result |0⟩ after T iterations, and thus correctly identifying that there is a bomb without exploding it, is given by

The authors state that the ability to obtain information about the bomb's functionality without ever "touching" it appears to be a paradox that, they argue, is based on the assumption that there is only a single "real" result.

[3] But according to the many-worlds interpretation, each possible state of a particle's superposition is real.

The authors therefore argue that the particle does actually interact with the bomb and it does explode, just not in our "world".

[5] Jean Bricmont offered an interpretation of the Elitzur–Vaidman bomb test in terms of Bohmian mechanics.

[11] It has also been argued that the bomb test can be constructed within the Spekkens toy model, suggesting that it is a less dramatic illustration of non-classicality than other quantum phenomena like the violation of Bell inequalities.

[12] The argument from Spekkens toy model involves the detector being able to detect a photon as either

yet still carry information, allowing the bomb test to be interpreted in classical terms.

[13] In 1994, Anton Zeilinger, Paul Kwiat, Harald Weinfurter, and Thomas Herzog performed an equivalent of the above experiment, proving interaction-free measurements are indeed possible.

[14] In 1996, Kwiat et al. devised a method, using a sequence of polarising devices, that efficiently increases the yield rate to a level arbitrarily close to one.

[14][15] It can also be argued that this revised construction is simply equivalent to a resonant cavity and the result looks much less shocking[to whom?]

In 2016, Carsten Robens, Wolfgang Alt, Clive Emary, Dieter Meschede, and Andrea Alberti[16] demonstrated that the Elitzur–Vaidman bomb testing experiment can be recast in a rigorous test of the macro-realistic worldview based on the violation of the Leggett–Garg inequality using ideal negative measurements.

In their experiment they perform the bomb test with a single atom trapped in a polarization-synthesized optical lattice.

This optical lattice enables interaction-free measurements by entangling the spin and position of atoms.

Bomb-testing problem diagram. A – photon emitter, B – bomb to be tested, C, D – photon detectors. Mirrors in the lower left and upper right corners are semi-transparent .
Figure 1: An illustration of the experiment using a Mach–Zehnder interferometer
Figure 2: Legend for Fig. 1
Figure 3: Once the photon encounters the beam splitter it enters a superposition wherein it both passes through and reflects off the half-silvered mirror
Figure 4: If the bomb is live, it will absorb the photon and detonate. If it is a dud, the photon is unaffected and continues along the lower path.
Figure 5 As in Figure 4, the photon travels the lower path toward the bomb, but in a superposition, where it also travels the upper path.
Figure 6: The second half-silvered mirror and the two detectors are positioned so that the photon will only arrive at Detector C if there is wave interference. This is only possible if the bomb is a dud.
Figure 7: If the bomb is live, and the photon took the upper path, there is no chance of interference at the second half-silvered mirror, and so, just as was the case at the first, it has an equal chance of reflecting off it or passing through it and arriving at either detector C or D. This is the only way it can arrive at D, signifying a live (unexploded) bomb.